The present invention is directed to a method of operating a discharge lamp system and a discharge lamp system in which vertical segregation is reduced.
Vertical operation of a discharge lamp system can lead to vertical segregation of vapor phase species, which in turn leads to color separation over the length of the lamp, reduced light output, local overheating of the lamp wall, and other problems that may cause premature lamp failure or unsatisfactory lamp performance. This is particularly true for high aspect ratio lamps (lamps whose length to width ratio is high).
A solution to this problem is proposed in U.S. Pat. No. 6,124,683 in which an arc in a discharge lamp is straightened by acoustic modulation of lamp power. Such power modulation can also provide some control over vertical segregation during vertical operation of the lamp.
As is now known, modulation of lamp power causes modulation of the arc temperature distribution and, as a result, modulation of the gas pressure distribution throughout the lamp. Certain frequencies of modulation cause standing wave oscillation of the gas pressure in the discharge tube of the lamp system. Acoustic modes in discharge lamp systems are generally determined based on a cylinder of a size comparable to the discharge tube of the lamp. If the pressure has a spatial dependence along the axis of the tube, then the acoustic mode is longitudinal. The number of half wavelengths determines the particular mode number. If there are two half wavelengths, the lamp is operating at the second longitudinal mode. If the pressure has a spatial dependence along the radius of the tube, then the acoustic mode is radial, and if the pressure has a spatial dependence around the circumference of the tube, then the acoustic mode is azimuthal. Combination acoustic modes are also possible, such as the radial-longitudinal mode and the azimuthal-longitudinal mode, in which the pressure distribution depends on more than one coordinate. These combination modes can be further defined, depending on the number of half wavelengths, such as a combination acoustic mode of the third azimuthal and second longitudinal modes.
The frequencies for each of these acoustic modes (the resonance frequencies) are determinable from the dimensions of the discharge tube and the speed of sound in the gas phase of the lamp. The speed of sound has a temperature dependence and the arc temperature profile can depend on position. Nevertheless, the resonance frequencies can be reasonably estimated using an isothermal cylindrical model.
The longitudinal mode frequencies are roughlyfnL=(nC)/(2Length),where fnL is the nth longitudinal mode, C is the average speed of sound, and Length is the cavity length.
The radial mode frequencies are roughlyfnR=(knRC)/(πD)where fnR is the nth radial mode, knR is a constant that is known for each radial mode (it is 3.83 for the first radial mode and higher for subsequent modes), C is the average speed of sound, and D is the diameter of the cavity.
The azimuthal mode frequencies are roughlyfnA=(knAC)/(πD)where fnA is the nth azimuthal mode, knA is a constant that is known for each azimuthal mode (it is 1.84 for the first azimuthal mode, 3.05 for the second, 4.20 for the third and higher for subsequent modes), C is the average speed of sound, and D is the diameter of the cavity.
Better estimates of the resonance frequencies can be obtained from finite element calculations of the eigenmodes of vessels approximating the shape of the cavity in which the arc is formed using well estimated temperature and composition distributions.
Still other methods of estimation are possible. For example, for a radial acoustic mode, the continuous radial sound speed profile can be discretized into iso-speed concentric cylinders. A characteristic time can be calculated for each cylinder by inverting the first radial resonant frequency for that cylinder. The composite characteristic time can be calculated from the sum of the individual cylinder's characteristic times. The refined estimate of the frequency of the first radial acoustic mode can be calculated from the inverted composite characteristic time.
Further, the resonance frequencies can be tuned based on visual clues such as accumulation of salt fill in patterns on the walls of the arc tube, and the disappearance of color separation. For example, salt rings may appear around the tube when the frequencies are properly tuned to longitudinal resonances.
Combination modes can be determined by combining the frequencies of the individual modes in quadrature so long as one of the modes is longitudinal. For example, the resonance frequency of the first radial and fourth longitudinal combination mode is
 f1R4L2=f1R2+f4L2.
The frequencies discussed herein are the power modulation frequencies (denoted herein “power frequencies”). For a sine waveform, the corresponding current (or voltage) frequencies are one-half the power frequencies.
With reference again to the prior art, a further solution to the problem of vertical segregation is offered in U.S. Pat. No. 6,184,633. As shown in FIG. 1, the lamp power is modulated in a repeating pattern of a sine wave sweeping over a frequency range 10 that is appropriate for arc-straightening and a lower frequency 12 corresponding to a longitudinal mode. The swept power frequency range is 90-110 kHz and the power frequency of the longitudinal mode is 24.5 kHz (the current frequencies being one-half these power frequencies). This improved control over the arc, but the lower frequency is difficult to generate efficiently and is too close to audio frequencies.
A further improvement is offered in U.S. Pat. No. 6,437,517 in which the repeating pattern of FIG. 1 is the same, except the lower frequency is replaced with a frequency higher than the arc-straightening frequency sweep. The higher frequency can be a single frequency or may sweep over a frequency range. The higher frequency excites a combination acoustic mode that combines the azimuthal mode (specifically, the third azimuthal mode or higher) and the longitudinal mode (specifically, the nth longitudinal mode). For a lamp 19 mm long and with an inner diameter of 4 mm, the arc-straightening frequency range is 90-110 kHz, the combination mode is centered on 150 kHz (±10 kHz) and the pattern is repeated at about 100 Hz. Due to its symmetry, this combination acoustic mode of the azimuthal and longitudinal modes is still difficult to excite and the present inventors have sought a suitable substitute combination acoustic mode that is easier to excite.